Date of Award

Summer 2014

Degree Type


Degree Name

Doctor of Philosophy (PhD)


Mechanical Engineering

First Advisor

Steven H. Frankel

Committee Chair

Steven H. Frankel

Committee Member 1

Jun Chen

Committee Member 2

Steven T. Wereley

Committee Member 3

Tom I. Shih


Electroosmotic flow with electrokinetic effects is the primary method of fluid handling in micro-total analysis systems. Under external applied electric fields, electrokinetic micro-devices allow for innovative functionality in a wide range of microfluidic applications including sample injection, separation, rapid micromixing, and miniaturized chemical and biochemical analysis and detection. This dissertation focuses on simulations of two electrokinetic phenomena, isotachophoresis (ITP) and electrokinetic instability (EKI). A set of coupled governing equations including the incompressible Naiver-Stokes equations, Nernst-Planck transport equations and a charge conservation equation are solved in the simulation. A multiblock in-house solver based on high-order finite difference schemes is developed to solve the system of equations and thus to numerically capture essential physics of ITP and EKI in microfluidic devices. Validation of the solver is provided for one-dimensional ITP problems in which sharp gradients present in species concentration and electric fields. It is demonstrated that the current solver can offer an accurate non-oscillatory solution with reduced numerical diffusion compared to several existing numerical schemes on a given uniform grid. Two-dimensional ITP and EKI problems are then simulated to acquire a good understanding of the basic mechanism and behavior of the two electrokinetic phenomena under certain conditions. Finally, a series of three-dimensional simulations are carried out to predict EKI phenomena in a realistic cross-shaped microchannel. It is shown that the current solver has the capability to capture the threshold value of applied electric field for the onset of instabilities and it offers a better prediction for the critical features of EKI phenomena in the considered cross-shaped microchannel compared to the numerical and experimental results presented in the literature. Moreover, in the general parametric study the present solver also explores several useful guidelines showing the effect of different parameters, including the electric field strength, the conductivity ratio, the channel depth as well as the electric field ratio on EKI in a cross-shaped microchannel.